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A194869 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194868; an interspersion.

%I A194869 #8 Mar 30 2012 18:57:44
%S A194869 1,3,2,5,4,6,9,7,10,8,14,12,15,13,11,19,17,21,18,16,20,26,23,28,25,22,
%T A194869 27,24,34,31,36,33,30,35,32,29,42,39,45,41,38,44,40,37,43,52,48,55,51,
%U A194869 47,54,50,46,53,49,62,58,65,61,57,64,60,56,63,59,66,74,69,77
%N A194869 Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194868; an interspersion.
%C A194869 Every pair of rows eventually intersperse.
%e A194869 Northwest corner:
%e A194869 1...3...5...9...14..19
%e A194869 2...4...7...12..17..23
%e A194869 6...10..15..21..28..36
%e A194869 8...13..18..25..33..41
%e A194869 11..16..22..30..38..47
%e A194869 20..27..35..44..54..64
%t A194869 r = -(1 + Sqrt[3])/2;
%t A194869 t[n_] := Table[FractionalPart[k*r], {k, 1, n}];
%t A194869 f = Flatten[Table[Flatten[(Position[t[n], #1] &) /@
%t A194869 Sort[t[n], Less]], {n, 1, 20}]]  (* A194868 *)
%t A194869 TableForm[Table[Flatten[(Position[t[n], #1] &) /@
%t A194869 Sort[t[n], Less]], {n, 1, 15}]]
%t A194869 row[n_] := Position[f, n];
%t A194869 u = TableForm[Table[row[n], {n, 1, 20}]]
%t A194869 g[n_, k_] := Part[row[n], k];
%t A194869 p = Flatten[Table[g[k, n - k + 1], {n, 1, 13},
%t A194869 {k, 1, n}]] (* A194869 *)
%t A194869 q[n_] := Position[p, n]; Flatten[Table[q[n],
%t A194869 {n, 1, 80}]]   (* A194870 *)
%Y A194869 Cf. A194832, A194868, A194870.
%K A194869 nonn,tabl
%O A194869 1,2
%A A194869 _Clark Kimberling_, Sep 04 2011